In digital communication systems, the digital information bits are mapped to symbols drawn from a finite set of discrete real or complex numbers. These symbols are used to modulate a radio frequency (RF) carrier's frequency, amplitude and/or phase. For example, a quadrature oscillator can be used to modulate the complex symbols onto the amplitude and phase of the RF carrier, and the signaling is referred to as Quadrature Amplitude Modulation (QAM). The time interval between symbols is referred to as the symbol or baud interval, and the inverse of this interval is referred to as the symbol or baud rate.
Most modem digital communication systems use a symbol rate that sends thousands or millions of symbols per second, over propagation media including satellite links through the earth's atmosphere, terrestrial links from towers to fixed or mobile land-based receivers, or wired links using ancient twisted-pair copper connections or more sophisticated fiber optic connections. Such media are dispersive, causing fading and reflections that result in multiple path delays arriving at the receiver. Such behavior is known as multipath, and causes symbols to smear across multiple symbol boundaries, which is referred to as inter-symbol interference (ISI). Moreover, mismatches in transmitter and receiver filtering induce ISI. Noise is added to the received signal from transmitter and receiver component imperfections, and from sources through the propagation path. At the receiver, an equalizer is used to mitigate the effects of ISI and noise induced in the entire channel, including transmitter, propagation medium, and front-end receiver processing. Since the exact channel characteristics are not known apriori at the receiver, the equalizer is usually implemented with adaptive methods.
A common type of equalizer uses adaptive filters, and the adjustment of filter coefficients can be done in a variety of ways. Trained equalization methods rely on the embedding of a pre-determined sequence in the transmitted data, referred to as a training or reference sequence. The receiver stores or generates a replica of the training sequence, and to the extent that the received sequence differs from the training sequence, an error measure is derived to adjust equalizer coefficients. Usually, equalizer coefficient convergence relies on multiple transmissions of the training sequence, and the channel characteristics are also time varying. Hence, periodic re-training is necessary.
A common method of trained coefficient adaptation uses the Least Mean Squares (LMS) algorithm, which minimizes a Mean Squared Error (MSE) cost function with a stochastic gradient descent update rule as described in a paper entitled “The complex LMS algorithm,” by Widrow, McCool, and Ball, in The Proceedings of the IEEE, vol. 63, no. 4, pp. to 719-720, April 1975.
Unfortunately, the training sequence needed for LMS takes up valuable bandwidth that could be used for data transmissions. Hence, methods that do not rely on a reference signal, or derive a reference signal from the data itself, are desirable. Such methods are referred to as blind equalization methods. A common blind equalization method replaces the reference signal in the LMS algorithm with the receiver's best guess at the data, and is therefore referred to as Decision Directed LMS (DD-LMS), as proposed in a paper entitled “Techniques for adaptive equalization of digital communication systems,” by R. W. Lucky, in the Bell Systems Technical Journal, vol. 45, no. 2, pp. 255-286, February 1966. Unfortunately, DD-LMS needs a reasonably low percentage of incorrect decisions to prevent algorithm divergence, and is therefore impractical from a cold-start initialization. Other blind algorithms are usually used from a cold-start.
The Constant Modulus Algorithm (CMA), proposed independently by Godard and Treichler (“Self-recovering equalization and carrier tracking in two-dimensional data communication systems,” by. D. N. Godard, in IEEE Transactions on Communications, vol. 28, no. 11, pp. 1867-1875, October 1980, and “A new approach to multipath correction of constant modulus signals,” by J. R. Treichler, and B. G. Agee, in IEEE Transactions on Acoustics, Speech, and Signal Processing, vol. ASSP-31, no. 2, pp. 459-472, April 1983) has rapidly become the most popular blind equalization algorithm in practice, and is well-studied in the archival literature, due to its robustness to realistic signaling environments and LMS-like computational complexity and asymptotic performance. Instead of minimizing a MSE cost function, CMA minimizes a quartic Constant Modulus (CM) cost function that penalizes dispersion at the equalizer output.
Though both LMS and CMA were originally introduced using a linear transversal, or finite impulse response (FIR) equalizer structure, a Decision Feedback Equalizer (DFE) is generally believed to provide superior ISI cancellation with less noise gain than an FIR equalizer structure. A DFE acts to additively cancel ISI by subtracting filtered decisions (or best guesses, also known as hard decisions) from the sampled received signals. The feedback structure embeds a FIR filter in a feedback loop, fed by symbol estimates, and therefore has infinite impulse response (IIR). Like the DD-LMS algortihm, the DFE architecture requires a low percentage of incorrect decisions to prevent algorithm divergence and error propagation, a phenomenon whereby an incorrect decision causes more incorrect decisions due to the recursive structure of the DFE. Therefore, a DFE requires alternative adaptive strategies from a cold-start. Several techniques based on adaptive IIR filtering have been proposed as summarized in a chapter entitled “Current approaches to blind decision feedback equalization,” by R. A. Casas et al., in the textbook, “Signal processing advances in wireless and mobile communications: trends in channel estimation and equalization,” edited by G. Giannakis, et al., Prentice Hall, Upper Saddle River, N.J., 2000.
Though adaptive IIR filtering approach for blind DFE initialization can achieve successful cold start up, its performance is significantly less optimal than DD-LMS/DFE and mechanical switch from IIR adaptation to DD-LMS adaptation usually exhibits performance degradation in transient period, and thus, in dealing with time varying channels. In order to achieve better transition between IIR adaptation and DD-LMS/DFE Endres et. al in Provisional Application No. 60,341,931, filed Dec. 17, 2001 entitled “Self-initializing decision feedback equalizer with automatic gain control” proposed linearly combining IIR adaptation and DD-LMS adaptation of the DFE coefficients.
On the other hand, it has been recognized that DFE is not robust under severe noise environment due to error propagation rooted in its recursive structure. Recent studies such as in “Joint Coding and Decision Feedback Equalization for Broadband Wireless Channels,” by Ariyavisitakul et at in IEEE Journals on Selected Areas in Comm. Vol. 16, No. 9, December 1998 proposed a soft decision device approach to reduce MSE of DFE output by replacing the hard decisions with cleverly estimated soft decisions.
The present invention combines the soft decision device approach and the seamless transition between IIR adaptation and DD-LMS adaptation. Unlike the linear combination of IIR and DD-LMS adaptations, this present invention uses a family of non-linear soft decision devices approximating the optimal soft decision device studied in soft-decision DFE literatures. According to the selection rule inferred from the non-linear soft decision device, DFE coefficients are updated by selected error signals between IIR adaptation and DD-LMS adaptation on a symbol-by-symbol basis, which jointly optimizes the soft decision device and DFE adaptation.